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Properties

Label 1512.2.r
Level $1512$
Weight $2$
Character orbit 1512.r
Rep. character $\chi_{1512}(505,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $36$
Newform subspaces $6$
Sturm bound $576$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.r (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(576\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1512, [\chi])\).

Total New Old
Modular forms 624 36 588
Cusp forms 528 36 492
Eisenstein series 96 0 96

Trace form

\( 36 q + O(q^{10}) \) \( 36 q - 14 q^{11} - 12 q^{17} - 12 q^{19} - 4 q^{23} - 18 q^{25} + 12 q^{29} + 24 q^{35} + 6 q^{41} + 6 q^{43} + 12 q^{47} - 18 q^{49} - 48 q^{53} - 14 q^{59} + 16 q^{65} + 6 q^{67} - 24 q^{71} + 36 q^{73} + 8 q^{77} - 16 q^{83} - 24 q^{85} + 48 q^{89} - 12 q^{95} - 42 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1512, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1512.2.r.a 1512.r 9.c $2$ $12.073$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
1512.2.r.b 1512.r 9.c $2$ $12.073$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
1512.2.r.c 1512.r 9.c $6$ $12.073$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{18}+\zeta_{18}^{2})q^{5}+(-1+\zeta_{18}+\cdots)q^{7}+\cdots\)
1512.2.r.d 1512.r 9.c $8$ $12.073$ 8.0.508277025.1 None \(0\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}+\beta _{4}-\beta _{5}+\beta _{7})q^{5}+\beta _{5}q^{7}+\cdots\)
1512.2.r.e 1512.r 9.c $8$ $12.073$ 8.0.2091141441.1 None \(0\) \(0\) \(3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2}+\beta _{3})q^{5}-\beta _{3}q^{7}+(\beta _{1}+2\beta _{3}+\cdots)q^{11}+\cdots\)
1512.2.r.f 1512.r 9.c $10$ $12.073$ 10.0.\(\cdots\).1 None \(0\) \(0\) \(3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{7})q^{5}-\beta _{1}q^{7}+(\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1512, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)